<p>
  First let's start with the concept of <strong>random variable</strong>. A random variable can be thought of as a drawing from a distribution whose outcome prior to the draw is uncertain. Imagine rolling a dice, you know that your chance of getting each is 1/6, but you don't know what's the number of your next roll is. If we roll the dice N times and record the number of each roll, a collection of those numbers is called <strong>discrete random variable</strong>. A discrete variable can take on a finite number of values. For our example, we can only take numbers from {1,2,3,4,5,6}. The other kind of variable is <strong>continuous random variable</strong>. A continuous variable can take on any value in a given range. You can think the rate of return as a continuous variable, it theoretically can take any value from \((-\infty, +\infty)\).
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